Subgroups — C₃×C₅×#2168 #14275202

Order 1920.

328 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2168	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
12	C₃×C₅×M₃₂	—	2	2	no	—
13	C₂×C₃×C₅×C₁₆	—	2	2	no	—
14	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
19	C₃×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
20	C₃×C₅×C₂²⋊C₈	C₄	1	1	yes	characteristic
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×#2168	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×C₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
25	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic
26	C₅×C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×C₂²⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×C₂²⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#346	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×D₄	C₈	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×C₈	—	2	1	no	—
34	C₂×C₃×C₅×C₈	—	2	1	no	—
35	C₂×C₃×C₅×C₈	—	2	1	no	—
36	C₂×C₃×C₅×C₈	—	2	1	no	—
37	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
43	C₃×C₅×C₂²⋊C₄	C₈	1	1	yes	characteristic
44	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₁₆	—	2	1	no	—
46	C₃×C₅×C₁₆	—	2	1	no	—
47	C₃×C₅×C₁₆	—	2	1	no	—
48	C₃×C₅×C₁₆	D₄	1	2	yes	complemented
49	C₂×C₃×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂²×C₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
51	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic
52	C₃×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
53	C₃×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
55	C₃×#346	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
58	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
59	C₅×M₃₂	—	2	2	no	—
60	C₂×C₅×C₁₆	—	2	2	no	—
61	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₁₆	C₂²×C₃	1	1	yes	characteristic
65	C₅×C₄⋊C₈	C₃×C₄	1	1	yes	characteristic
66	C₅×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic
67	C₅×C₂²⋊C₈	C₃×C₄	1	1	yes	characteristic
68	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	#2168	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂×C₈	1	1	yes	characteristic
72	C₃×C₅×D₄	—	2	2	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	1	no	—
75	C₂×C₃×C₄×C₅	—	2	1	no	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
82	C₃×C₅×C₈	—	2	1	no	—
83	C₃×C₅×C₈	—	2	1	no	—
84	C₃×C₅×C₈	—	2	1	no	—
85	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
86	C₃×C₅×C₈	#41	1	1	yes	characteristic
87	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
88	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
89	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
90	C₃×M₃₂	—	2	2	no	—
91	C₂×C₃×C₁₆	—	2	2	no	—
92	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic
96	C₃×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
97	C₃×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic
98	C₃×C₂²⋊C₈	C₄×C₅	1	1	yes	characteristic
99	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
100	C₂×C₅×D₄	C₃×C₈	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
103	C₂×C₅×C₈	—	2	1	no	—
104	C₂×C₅×C₈	—	2	1	no	—
105	C₂×C₅×C₈	—	2	1	no	—
106	C₂×C₅×C₈	—	2	1	no	—
107	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
109	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
110	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₃×C₈	1	1	yes	characteristic
112	C₅×C₂²⋊C₄	C₃×C₈	1	1	yes	characteristic
113	C₅×C₂²⋊C₄	C₃×C₈	1	1	yes	characteristic
114	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
115	C₅×C₁₆	—	2	1	no	—
116	C₅×C₁₆	—	2	1	no	—
117	C₅×C₁₆	—	2	1	no	—
118	C₅×C₁₆	C₃×D₄	1	2	yes	complemented
119	C₂×M₃₂	C₂×C₃×C₅	1	1	yes	characteristic, complemented
120	C₂²×C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
121	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic
122	C₄⋊C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
123	C₂²⋊C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
124	C₂²⋊C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
125	#346	C₂×C₃×C₅	1	1	yes	characteristic, complemented
126	C₂²×C₃×C₅	—	2	1	no	—
127	C₂²×C₃×C₅	—	2	1	no	—
128	C₂²×C₃×C₅	—	2	1	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	—	2	1	no	—
131	C₂²×C₃×C₅	M₃₂	1	2	yes	complemented
132	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
133	C₃×C₄×C₅	—	2	1	no	—
134	C₃×C₄×C₅	—	2	1	no	—
135	C₃×C₄×C₅	—	2	1	no	—
136	C₃×C₄×C₅	—	2	1	no	—
137	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
138	C₃×C₄×C₅	#131	1	1	yes	characteristic
139	C₂×C₃×D₄	C₅×C₈	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
142	C₂×C₃×C₈	—	2	1	no	—
143	C₂×C₃×C₈	—	2	1	no	—
144	C₂×C₃×C₈	—	2	1	no	—
145	C₂×C₃×C₈	—	2	1	no	—
146	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
147	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
148	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
149	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
150	C₃×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
151	C₃×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
152	C₃×C₂²⋊C₄	C₅×C₈	1	1	yes	characteristic
153	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
154	C₃×C₁₆	—	2	1	no	—
155	C₃×C₁₆	—	2	1	no	—
156	C₃×C₁₆	—	2	1	no	—
157	C₃×C₁₆	C₅×D₄	1	2	yes	complemented
158	C₂³×C₅	C₂×C₃×C₈	1	1	yes	characteristic
159	C₂³×C₅	C₂×C₃×C₈	1	1	yes	characteristic
160	C₅×D₄	—	2	2	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₃×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
170	C₅×C₈	—	2	1	no	—
171	C₅×C₈	—	2	1	no	—
172	C₅×C₈	—	2	1	no	—
173	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
174	C₅×C₈	C₃×#41	1	1	yes	characteristic
175	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
176	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
177	C₄×D₄	C₃×C₄×C₅	1	1	yes	characteristic
178	M₃₂	—	2	2	no	—
179	C₂×C₁₆	—	2	2	no	—
180	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
181	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
182	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
183	C₂×C₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
184	C₄⋊C₈	C₃×C₄×C₅	1	1	yes	characteristic
185	C₂²⋊C₈	C₃×C₄×C₅	1	1	yes	characteristic
186	C₂²⋊C₈	C₃×C₄×C₅	1	1	yes	characteristic
187	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
188	C₂×C₃×C₅	—	2	2	no	—
189	C₂×C₃×C₅	—	4	1	no	—
190	C₂×C₃×C₅	C₈×D₄	1	1	yes	characteristic
191	C₂×C₃×C₅	C₂×M₃₂	1	1	yes	characteristic
192	C₂×C₃×C₅	#504	1	1	yes	characteristic
193	C₂³×C₃	C₂×C₅×C₈	1	1	yes	characteristic
194	C₂³×C₃	C₂×C₅×C₈	1	1	yes	characteristic
195	C₃×D₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	1	no	—
199	C₂×C₃×C₄	—	2	1	no	—
200	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
202	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂×C₅×C₈	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
205	C₃×C₈	—	2	1	no	—
206	C₃×C₈	—	2	1	no	—
207	C₃×C₈	—	2	1	no	—
208	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
209	C₃×C₈	C₅×#41	1	1	yes	characteristic
210	C₂²×C₅	—	2	1	no	—
211	C₂²×C₅	—	2	1	no	—
212	C₂²×C₅	—	2	1	no	—
213	C₂²×C₅	—	2	1	no	—
214	C₂²×C₅	—	2	1	no	—
215	C₂²×C₅	C₃×M₃₂	1	2	yes	complemented
216	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
217	C₄×C₅	—	2	1	no	—
218	C₄×C₅	—	2	1	no	—
219	C₄×C₅	—	2	1	no	—
220	C₄×C₅	—	2	1	no	—
221	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
222	C₄×C₅	C₃×#131	1	1	yes	characteristic
223	C₂×D₄	C₃×C₅×C₈	1	1	yes	characteristic
224	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
226	C₂×C₈	—	2	1	no	—
227	C₂×C₈	—	2	1	no	—
228	C₂×C₈	—	2	1	no	—
229	C₂×C₈	—	2	1	no	—
230	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
231	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
232	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
233	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
234	C₄⋊C₄	C₃×C₅×C₈	1	1	yes	characteristic
235	C₂²⋊C₄	C₃×C₅×C₈	1	1	yes	characteristic
236	C₂²⋊C₄	C₃×C₅×C₈	1	1	yes	characteristic
237	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
238	C₁₆	—	2	1	no	—
239	C₁₆	—	2	1	no	—
240	C₁₆	—	2	1	no	—
241	C₁₆	C₃×C₅×D₄	1	2	yes	complemented
242	C₃×C₅	#2168	1	1	yes	characteristic, direct product factor, Hall
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	—	2	1	no	—
245	C₂²×C₃	—	2	1	no	—
246	C₂²×C₃	—	2	1	no	—
247	C₂²×C₃	—	2	1	no	—
248	C₂²×C₃	C₅×M₃₂	1	2	yes	complemented
249	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
250	C₃×C₄	—	2	1	no	—
251	C₃×C₄	—	2	1	no	—
252	C₃×C₄	—	2	1	no	—
253	C₃×C₄	—	2	1	no	—
254	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
255	C₃×C₄	C₅×#131	1	1	yes	characteristic
256	C₂×C₅	—	2	2	no	—
257	C₂×C₅	—	4	1	no	—
258	C₂×C₅	C₃×C₈×D₄	1	1	yes	characteristic
259	C₂×C₅	C₂×C₃×M₃₂	1	1	yes	characteristic
260	C₂×C₅	C₃×#504	1	1	yes	characteristic
261	C₂³	C₂×C₃×C₅×C₈	1	1	yes	characteristic
262	C₂³	C₂×C₃×C₅×C₈	1	1	yes	characteristic
263	D₄	—	2	2	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
269	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
270	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
271	C₂×C₄	C₂×C₃×C₅×C₈	1	1	yes	characteristic
272	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
273	C₈	—	2	1	no	—
274	C₈	—	2	1	no	—
275	C₈	—	2	1	no	—
276	C₈	C₂×C₃×C₅×D₄	1	1	yes	characteristic
277	C₈	C₃×C₅×#41	1	1	yes	characteristic
278	C₂×C₃	—	2	2	no	—
279	C₂×C₃	—	4	1	no	—
280	C₂×C₃	C₅×C₈×D₄	1	1	yes	characteristic
281	C₂×C₃	C₂×C₅×M₃₂	1	1	yes	characteristic
282	C₂×C₃	C₅×#504	1	1	yes	characteristic
283	C₅	C₃×#2168	1	1	yes	characteristic, direct product factor, Sylow
284	C₂²	—	2	1	no	—
285	C₂²	—	2	1	no	—
286	C₂²	—	2	1	no	—
287	C₂²	—	2	1	no	—
288	C₂²	—	2	1	no	—
289	C₂²	C₃×C₅×M₃₂	1	2	yes	complemented
290	C₂²	C₂²×C₃×C₅×C₈	1	1	yes	characteristic
291	C₄	—	2	1	no	—
292	C₄	—	2	1	no	—
293	C₄	—	2	1	no	—
294	C₄	—	2	1	no	—
295	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
296	C₄	C₃×C₅×#131	1	1	yes	characteristic
297	C₃	C₅×#2168	1	1	yes	characteristic, direct product factor, Sylow
298	C₂	—	2	2	no	—
299	C₂	—	4	1	no	—
300	C₂	C₃×C₅×C₈×D₄	1	1	yes	characteristic
301	C₂	C₂×C₃×C₅×M₃₂	1	1	yes	characteristic
302	C₂	C₃×C₅×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₅×C₈	C₂³
commutator	C₂²	C₂²×C₃×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂×C₃×C₅×D₄	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅×C₈ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×M₃₂	C₂	semidirect
2. C₂²×C₃×C₅×C₁₆	C₂	semidirect
4. C₃×C₅×C₄⋊C₁₆	C₂	semidirect
5. C₃×C₅×C₂²⋊C₁₆	C₂	semidirect
6. C₃×C₅×C₂²⋊C₁₆	C₂	semidirect
7. C₃×C₅×#346	C₂	semidirect
8. C₅×#2168	C₃	direct (N × H)
22. C₃×#2168	C₅	direct (N × H)
23. C₂×C₅×M₃₂	C₂×C₃	semidirect
24. C₂²×C₅×C₁₆	C₂×C₃	semidirect
26. C₅×C₄⋊C₁₆	C₂×C₃	semidirect
27. C₅×C₂²⋊C₁₆	C₂×C₃	semidirect
28. C₅×C₂²⋊C₁₆	C₂×C₃	semidirect
29. C₅×#346	C₂×C₃	semidirect
48. C₃×C₅×C₁₆	D₄	semidirect
49. C₂×C₃×M₃₂	C₂×C₅	semidirect
50. C₂²×C₃×C₁₆	C₂×C₅	semidirect
52. C₃×C₄⋊C₁₆	C₂×C₅	semidirect
53. C₃×C₂²⋊C₁₆	C₂×C₅	semidirect
54. C₃×C₂²⋊C₁₆	C₂×C₅	semidirect
55. C₃×#346	C₂×C₅	semidirect
69. #2168	C₃×C₅	direct (N × H)
118. C₅×C₁₆	C₃×D₄	semidirect
119. C₂×M₃₂	C₂×C₃×C₅	semidirect
120. C₂²×C₁₆	C₂×C₃×C₅	semidirect
122. C₄⋊C₁₆	C₂×C₃×C₅	semidirect
123. C₂²⋊C₁₆	C₂×C₃×C₅	semidirect
124. C₂²⋊C₁₆	C₂×C₃×C₅	semidirect
125. #346	C₂×C₃×C₅	semidirect
131. C₂²×C₃×C₅	M₃₂	semidirect
157. C₃×C₁₆	C₅×D₄	semidirect
215. C₂²×C₅	C₃×M₃₂	semidirect
241. C₁₆	C₃×C₅×D₄	semidirect
242. C₃×C₅	#2168	direct (N × H)
248. C₂²×C₃	C₅×M₃₂	semidirect
283. C₅	C₃×#2168	direct (N × H)
289. C₂²	C₃×C₅×M₃₂	semidirect
297. C₃	C₅×#2168	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×M₃₂	2
C₂²×C₃×C₅×C₁₆	2
C₃×C₅×C₈×D₄	2
C₃×C₅×C₄⋊C₁₆	2
C₃×C₅×C₂²⋊C₁₆	2
C₃×C₅×#346	2
C₅×#2168	3
C₃×#2168	5

Subgroups — C3×C5×#2168 #14275202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2168 #14275202